Limited Angle Reconstruction in Tomography via Squashing.

Area of Science:

• Image reconstruction
• Computational mathematics
• Applied physics

Background:

• Density reconstruction from projections is crucial in various scientific fields.
• Existing algorithms often require complete angular data, limiting their applicability.
• Limited-angle reconstruction poses significant mathematical challenges.

Purpose of the Study:

• To develop a new, practical algorithm for reconstructing a 2D density function.
• To address the challenge of density reconstruction using projections limited to angles greater than a fixed delta.
• To provide a simple and effective solution for limited-angle reconstruction problems.

Main Methods:

• The algorithm employs an affine (squashing) scale change on the density function.
• Projections of the transformed function are known at equally spaced angles.
• The transformed function is reconstructed, and then the original density is obtained by inverting the scale change.

Main Results:

• A novel algorithm for limited-angle density reconstruction is presented.
• The algorithm's performance is dependent on the angle threshold (delta) and the function's smoothness.
• The method provides a practical and simple solution for reconstructible density functions.

Conclusions:

• The proposed algorithm offers a viable approach for density reconstruction from limited angular projections.
• The technique is particularly useful when projections are only available above a specific angle.
• This method simplifies the reconstruction process by transforming the problem into one with known angular data.